1979 USAMO Problems/Problem 1: Difference between revisions
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[[Category:Olympiad Number Theory Problems]] | [[Category:Olympiad Number Theory Problems]] | ||
Revision as of 18:07, 3 July 2013
Problem
Determine all non-negative integral solutions 
if any, apart from permutations, of the Diophantine Equation 
.
Solution
Recall that 
for all integers 
. Thus the sum we have is anything from 0 to 14 modulo 16. But 
, and thus there are no integral solutions to the given Diophantine equation.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
See Also
| 1979 USAMO (Problems • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America. 
